{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.fftpack import fft\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fourier_transform(actions, T=0.002):\n",
    "    N = len(actions)\n",
    "    # print(N)\n",
    "    x = np.linspace(0.0, N*T, N)\n",
    "    y = actions\n",
    "    yf = fft(y)\n",
    "    freq = np.linspace(0.0, 1.0/(2.0*T), N//2)\n",
    "    amplitudes = 2.0/N * np.abs(yf[0:N//2])\n",
    "    # plt.plot(freq, amplitudes)\n",
    "    return freq, amplitudes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "Fs = 1e4      # 采样频率\n",
    "f1 = 390       # 信号频率1\n",
    "f2 = 2e3      # 信号频率2\n",
    "t=np.linspace(0., 1., int(Fs))   # 生成 1s 的实践序列   \n",
    "noise1 = np.random.random(int(1e4))      # 0-1 之间的随机噪声\n",
    "noise2 = np.random.normal(1.,10.,int(1e4))\n",
    "#产生的是一个10e3的高斯噪声点数组集合（均值为：1，标准差：10）\n",
    "y=2*np.sin(2*np.pi*f1*t)+5*np.sin(2*np.pi*f2*t)+noise2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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      "4983.996799359872 0.24935668527356422\n",
      "4984.996999399879 0.08806722127320672\n",
      "4985.9971994398875 0.3528290921847805\n",
      "4986.997399479896 0.17005377275500966\n",
      "4987.997599519904 0.10933961586329449\n",
      "4988.997799559912 0.1270026181780593\n",
      "4989.99799959992 0.032857617251449686\n",
      "4990.998199639927 0.04772298907829577\n",
      "4991.998399679936 0.17009744956323644\n",
      "4992.998599719944 0.12332323014815309\n",
      "4993.998799759952 0.24558149395796233\n",
      "4994.99899979996 0.11838489259795001\n",
      "4995.999199839967 0.05891152317919608\n",
      "4996.9993998799755 0.2444862263250142\n",
      "4997.999599919984 0.12216512794206069\n",
      "4998.999799959992 0.13946385901646263\n",
      "5000.0 0.2305708160050201\n"
     ]
    }
   ],
   "source": [
    "freqs, amps = fourier_transform(y, T=1/Fs)\n",
    "for a, b in zip(freqs, amps):\n",
    "    print(a, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f470905dd60>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(freqs, amps)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "dcs_py38",
   "language": "python",
   "name": "python3"
  },
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